(1) Technical Field
The present invention relates to risk management. More specifically, the present invention relates to a method, computer program product, and system for employing readily available, hazard data to estimate an expected repair cost for use in risk management, such as in seismic risk management.
(2) Description of Related Art
The field of seismic risk management has been gradually developing over the past few decades, increasingly enabled by technological advances in software and driven by a need for more informed property ownership decisions.
Seismic risk enters into several important real estate decision-making processes, such as the purchase of investment property, performance-based design of new structures, seismic rehabilitation of existing buildings, and decisions regarding the purchase of earthquake insurance. In such situations, example of important factors include who the decision-makers are, how they make decisions, what aspects of seismic risk most concern them, and the length of their planning horizon.
Economic seismic risk to large commercial properties in seismically active regions with commercial mortgages is assessed every time the property changes hands, typically on the order of every five to ten years. By contrast, a building is designed and built only once. Thus, the most common opportunities for market forces to bring about seismic-risk mitigation for commercial properties are at times of sale. Anecdotal evidence suggests that these are mostly missed opportunities, as risk is typically not mitigated, even in more vulnerable buildings.
This can be partly explained by considering the context in which seismic assessments are performed. During virtually every sale of an existing commercial building, the buyer assesses the building's investment value using a financial analysis that considers revenues and expenses, rent roll, market leasing, physical condition, and other property information. The investor makes his or her bidding decision based on projected income and expenses, using one or more of the economic performance metrics of net present value, net operating income, cash flow, internal rate of return, and capitalization rate.
The input to this financial analysis is typically provided by a real estate broker representing the seller, whose figures the investor checks and modifies during a due-diligence study. Many of the inputs are known values, such as the quantity of leases, duration, and income from current leases. However, many other values are uncertain. Vacancy rates, market rents, and other important parameters fluctuate significantly and unpredictably, leading to substantial uncertainty in the future economic performance of a property. In the face of these uncertainties, the bidder usually estimates investment value using best-estimate inputs and then again with deterministic sensitivity studies to probe conditions that would lead to poor performance (higher future vacancy rates, for example). The future cost to repair earthquake damage is not one of the parameters the bidder uses in the financial analysis. This is important because seismic risk is not a market quantity.
The real estate market is not wholly without forces to influence seismic-risk mitigation. The due-diligence study typically includes an engineering assessment of the condition of the property, which itself typically includes an estimate of the earthquake probable maximum loss (PML). PML is by far the dominant earthquake risk parameter in financial circles.
The earthquake PML has no standard quantitative definition. Most working definitions involve the level of loss associated with a large, rare event. One definition is that PML is the 90th percentile of loss given the occurrence of what building codes until recently called the design basis earthquake (DBE). The DBE is an event producing a shaking intensity with 10% exceedance probability in 50 years. Colloquially (and inexactly), this is an upper-bound loss given the 500-year earthquake. More accurately, assuming Poisson arrivals of earthquakes, this shaking level has a mean occurrence rate of 0.00211 yr−1 and a mean recurrence time of 475 years. Because this PML is the 90th percentile loss given this level of shaking, the PML-level loss can have a much longer mean recurrence time.
Commercial lenders often use PML to help decide whether to underwrite a mortgage. It is common, for example, for a commercial lender to refuse to underwrite a mortgage if the PML exceeds 20% to 30% of the replacement cost of the building, unless the buyer purchases earthquake insurance, a costly requirement that often causes the investor to decide against bidding. Once the PML hurdle is passed, the bidder usually proceeds to ignore seismic risk, for at least the following:
1. Irrelevant planning period. Investors plan on the order of 5 years, making loss corresponding to shaking intensity with a 500-year recurrence time largely irrelevant, too rare even for consideration in a sensitivity study.
2. Incompatibility with financial analysis. PML is a scenario value, not an ongoing cost that can be reflected in a cashflow analysis.
3. Custom. Investors are not required by custom or regulation to include seismic risk in the financial analysis.
Lacking any measure of economic risk beyond PML, the bidder has no basis for assessing how the seismic risk of a building should influence the purchase price or for judging whether seismic risk mitigation might be worth exploring. Faced with a high PML, the bidder might increase the discount rate used in the financial analysis to reduce the present value of the future net income stream.
Improving upon the prior art in order to increase the efficacy of seismic risk analysis, the Applicant previously filed application number 10/862,185, entitled, “Method, Computer Program Product, and System for Risk Management (hereinafter Application '185).” The prior application discloses a method for the calculation of economic seismic risk for buildings in terms of expected annualized loss (EAL) and a scenario loss estimate called probable frequent loss (PFL), both of which measure a building owner's risk of earthquake-damage repair costs. Application '185 disclosed that PFL can be reasonably estimated using a simplified performance-based earthquake engineering (PBEE) analysis that involves a single linear structural analysis and some simple calculations of loss conditioned on structural response.
It was shown that:EAL≈H·PFL,  (1)where
                              H          ≡                                    G              NZ                                      ln              ⁡                              (                                                      G                    NZ                                    /                                      G                    EBE                                                  )                                                    ,                            (        2        )            in which EAL is defined as the expected annualized value of repair cost to a particular building in a particular location and H is referred to as the economic hazard coefficient. The PFL is a scenario loss estimate: the estimated mean building repair cost conditioned on the occurrence of shaking in the economic-basis event, EBE. The EBE is defined as the event producing site shaking with 10% probability of exceedance in 5 years (Compare with the design-basis earthquake, DBE, whose shaking intensity has 10% exceedance probability in 50 yr.). The site shaking intensity of the EBE is denoted by sEBE. GEBE is the mean exceedance frequency at that site of the shaking intensity sEBE. GNZ refers to the mean exceedance frequency of the lowest shaking intensity sNZ that would produce a nonnegligible repair cost. The intensities sNZ and sEBE are measured in terms of damped elastic spectral acceleration at period T and damping ratio ζ.
Note that the methodology also produces reasonable estimates of EAL if EBE is defined slightly differently. For example, it was found that similar results are produced for EBE defined as the event producing site shaking with a 50% probability of exceedance in 50 years. The value of defining EBE as is done here (10% in 5 yr, rather than 50% in 50 yr) is for its relevance to the typical commercial real-estate investor, for whom 50 years is too long a planning period.
The methodology for calculating PFL, H, and EAL is expected to be of value to commercial real-estate investors and possibly other stakeholders of high-value buildings in seismically active regions. For example, it is useful in several identifiable ways:                a. Relevant scenario loss for the investor's sensitivity study. First, the PFL reflects a reasonable upper-bound loss within the typical investor's planning period (mean loss conditioned on shaking with 10% exceedance probability in 5 years). This is in contrast with the commonly-estimated probable maximum loss (PML), which tends to reflect a loss associated with the DBE. While shaking and loss with 500-yr or longer return period is far too rare to be of interest to the typical commercial investor, PFL could be reasonably employed in the investor's sensitivity studies. The investor typically examines impact on investment value (measured, e.g., by return on equity) under various what-if situations, such as future vacancy rates that are higher than expected, or market rents that are lower than expected. The investor would know that PFL could calculate by how much return on equity is reduced if the EBE occurs.        b. Investor can reflect seismic risk as an operating expense. PFL can be multiplied by H to produce EAL, which can be readily employed as an operating expense in the investor's financial analysis. Banks are already beginning to quantify their seismic risk in terms of EAL; real-estate investors may not be far behind.        c. Short learning curve for investor and engineering consultant. PFL is conceptually very similar to PML, and should be readily understood both by investors who already understand PML, and by engineering consultants who currently estimate PML for investors. EAL should also be readily understood by investors as amortized seismic risk. The investor need not understand seismic vulnerability nor seismic hazard, and the engineering consultant need not create a complete seismic vulnerability function or seismic hazard function.        d. A new consulting product for little extra work. The engineer who estimates PML can at the same time estimate PFL using the same information and procedures. By looking up H on a paper map or electronic database, and calculating EAL as the product of H and PFL, the consultant can provide his or her client with valuable new information for little additional effort. The same maps and database can, incidentally, provide the consultant with EBE and DBE shaking intensity.        
While the prior invention presented a method to calculate seismic risk management by calculating PFL and EAL, given sNZ, GNZ, sEBE, and GEBE, it did not provide a method for calculating GNZ, sEBE, GEBE. Thus, a continuing need exists for a system and methodology for employing readily available, gridded hazard data to calculate GNZ, sEBE, GEBE, and thereby H, for any geographic location and fundamental period (T) within the boundaries of the gridded data.